Answered: If = [10 m, 30°] and = [25 m, 130°],…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 20CQ: If two vectors have the same magnitude, do their components have to be the same?

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Question

If = [10 m, 30°] and = [25 m, 130°], what is the direction of the sum of these two vectors (in degrees from the positive x-axis)?

Expert Solution

Step 1

Given data

The magnitude of the vector A is given as $|A| = 10 m$ .
The direction of vector A is given as $θ_{A} = 30 °$ .
The magnitude of the vector B is given as $|B| = 25 m$ .
The direction of vector B is given as $θ_{B} = 130 °$ .

The vector equation for vector A is obtained as,

$\vec{A} = (|A| \cos θ_{A}) \hat{i} + (|A| \sin θ_{A}) \hat{j} \vec{A} = (10 \cos 30 °) \hat{i} + (10 \sin 30 °) \hat{j} \vec{A} = 8.66 \hat{i} + 5 \hat{j}$

The vector equation for vector A is obtained as,

$\vec{B} = (|B| \cos θ_{B}) \hat{i} + (|B| \sin θ_{B}) \hat{j} \vec{B} = (25 \cos 130 °) \hat{i} + (25 \sin 130 °) \hat{j} \vec{B} = - 16.07 \hat{i} + 19.15 \hat{j}$

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